Methods for the detection of objects of the generic type are already well known from the practice. Object characteristics can be, for example, the width, the position and the brightness of the structure on the object and/or the brightness of the object itself. All the characteristics referred to are ultimately based on the detection of brightness, since the accuracy with which a width and a position of an object is obtained is also determined by the varying brightness or detected brightness.
In industrial applications, such as in the metrology of line widths or positions on substrates in the semiconductor industry, coordinate measuring machines are utilized of the type described, for example, in German Patent Application DE 198 19 492. This measuring device is used for high-precision measurement of the coordinates of structures on substrates, for example, masks, wafers, flat panel displays and vapor deposited structures, in particular however, for transparent substrates. The coordinates are determined relative to a reference point to within just a few nanometers. Herein, for example, an object is illuminated with light from a mercury-vapor lamp and is imaged onto a CCD chip of a camera by means of an imaging optics. The CCD chip usually records a plurality of images of the same object using the same exposure time. It is thus of particular importance that the varying brightness (intensity) of the light source generates a linear response on the detector.
German Patent Application DE 101 31 897 also deals with the problem of varying results obtained from the repeated measurement of position and in particular line widths of the coordinate measuring machine using different exposure times and/or with varying brightness emitted by the light source. In this patent application, the problem is solved by variations in the imaging process, more precisely by applying an averaging procedure to the varying error amount, to reduce the error source. In practice, however, the residual error is still relatively large even after error reduction.
In the search for new solutions with smaller residual errors, it should be kept in mind that fluctuations in the exposure time and/or fluctuations in the brightness of the light source are unavoidable, even if reduced to a low level. One reason for this residual error is the non-linearity of the detector or light sensor (the CCD chip of a camera in the case of a coordinate measuring machine), which depending on the brightness emitted by the light source changes the form of the detected image to such an extent that variations in the values measured on the structures arise. If repeatable measurements for the determination of object characteristics (e.g. position, line width and brightness) are to be made, then the measuring results for the object characteristics must be free of these influences. For the qualitative measurement of an image, in particular—but not only—for the position and line width measurement on semiconductor substrates, the measuring result should therefore only be influenced by the object, e.g. a wafer or a mask, rather than by the randomness of the measuring process such as, for example, the exposure time and the brightness emitted by the light source.
As is well known from general technical knowledge, there are evaluation algorithms which independent of the original brightness measuring result N and the values obtained for black (no light), always deliver the same result for the position and in particular for line widths of structures. Mathematically formulated, the result is thus independent of a linear transformation of the originally detected brightness measuring results. If the originally detected brightness measuring results N are transformed by a freely selectable linear function such as N′=aN+b with linearity parameters a and b, the result, for example the line width and the line position, does not change. Thus all the linear variations of the originally detected brightness measuring results are practically harmless with regard to a possible deformation of the detected image.
This linear transformation of the originally detected brightness measuring results N is in most cases only approximate, however. On the contrary existent measuring systems, such as the light sensor mentioned above, exhibit non-linearities which are small in the case of a good system, but which cannot be disregarded when a very precise measurement is required.